It has become standard practice to plan wells and analyze bit performance using log-based rock strength analysis. There are several methodologies in use that characterize rock strength in terms of CCS, but the most widely used standard by drill bit specialists is “unconfined” compressive strength (UCS). UCS generally refers to the strength of the rock when the rock is under only limited or uniaxial loading. The strength of the rock is typically increased when the rock is supported by confining compressive pressures or stresses from all directions. This strength is expressed in terms of CCS, which is force per unit area, i.e., pounds per square inch (psi).
The use of UCS for bit selection and bit performance prediction/analysis is somewhat problematic in that the “apparent” strength of the rock to a bit is typically something different than UCS. There is an awareness of the problem, as it is widely accepted and documented that bit performance is greatly influenced by drilling fluid pressure and the difference between drilling fluid pressure and the in situ pore pressure (PP) of the rock being drilled. The pressure provided by the drilling fluid is often referred to as the equivalent circulating density (ECD) pressure and may be expressed in terms of mud weight, i.e. pounds per gallon (ppg). For vertical wells, the drilling fluid pressure or ECD pressure replaces the overburden (OB) pressure as the overburden is drilled away from the rock.
One widely practiced and accepted “rock mechanics” method for calculating CCS is to use the following mathematical expression:CCS=UCS+DP+2Dp sin FA/(1−sin FA)  (1)                where: UCS=the unconfined compressive strength of the rock;                    DP=differential pressure (or confining stress on on the rock); and            FA=internal angle of friction of the rock or friction angle (a rock property).                        
Adapting equation (1) to the bottom hole drilling condition for highly permeable rock is often performed by defining the DP as the difference between the ECD pressure applied by a drilling fluid upon the rock being drilled and the in-situ PP of the rock before drilling.
This adaptation results in the following expression for the CCS for high permeability rock (CCSHP):CCSHP=UCS+DP+2DP sin FA/(1−sin FA)  (2)where: DP=ECD pressure−in situ pore pressure.  (3)
In the case of rock which is very low in permeability, there is no industry wide standard or methodology to predict the apparent strength of the rock to the bit. There have been various schemes proposed, but the only simple methods that have gained limited acceptance assume the rock behaves as if permeable or that the PP in the rock is zero. The latter assumption results in the following mathematical expression for the CCSLP for low permeability rock:CCSLP=UCS+DP+2DP sin FA/(1−sin FA)  (4)where: DP=ECD pressure−0.  (5)
The assumption that PP is zero and that the differential pressure DPECD is generally equal to the ECD pressure for low permeability rock often leads to erroneous estimates for the apparent CCSLP. Subsequent use of these CCSLP estimates for low permeability rock then leads to poor estimates when the CCSLP estimates are used for bit selection, drill bit rate of penetration calculations, bit wear life predictions, and other like estimates based on the strength of the rock.
Another drawback to the above method for calculating CCS is that it fails to account for the change in the stress state of the rock for deviated or horizontal wellbores relative to vertical wellbores. Wellbores drilled at deviated angles or as horizontal wellbores can have a significantly different stress state in the depth of cut zone due to pressure applied by overburden as compared to vertical wellbores wherein the overburden has been drilled away.
Still yet another shortcoming is that CCS as calculated above is an average strength value across the bottom hole profile of a wellbore assuming that the profile is generally flat. In actuality, the bottom hole profiles of the wellbores can be highly contoured depending on the configuration of the bits creating the wellbore. Further, stress concentrations occur about the radial periphery of the hole. Highly simplified methods of calculating CCS fail to take into account these geometric factors which can significantly change the apparent strength of the rock to a drill bit during a drilling operation under certain conditions.
Accordingly, there is a need for a better way to calculate CCS for rocks subject to drilling, and more particularly, for rocks which have low permeability. The method should account for the relative change in pore pressure (ΔPP) due to the drilling operation rather than assume the PP will remain at the PP of the surrounding reservoir in the case of highly permeable rock or assume there is no significant PP in the rock for the case of very low permeability rock. The present invention addresses this need by providing improved methods for estimating CCS for low permeability rocks and for rocks that have limited permeability. Further, the present invention addresses the need to accommodate the altered stress state in the depth of cut zone found in deviated and horizontal wellbores as compared to those of vertical wellbores. Additionally, the present invention provides a way to accommodate geometric factors such as wellbore profiles and associated stress concentrations that can significantly affect the apparent CCS of rock being drilled away to create a wellbore.